Let's solve the inequality step by step, based on the image you provided.
---
Problem:
Solve the inequality:
$$
0 > 3x - 3 - 6
$$
---
Step 1: Simplify the right-hand side
Combine like terms:
$$
3x - 3 - 6 = 3x - 9
$$
So the inequality becomes:
$$
0 > 3x - 9
$$
---
Step 2: Add 9 to both sides
$$
0 + 9 > 3x - 9 + 9
$$
$$
9 > 3x
$$
---
Step 3: Divide both sides by 3
$$
\frac{9}{3} > x
$$
$$
3 > x
$$
Or equivalently:
$$
x < 3
$$
---
Step 4: Graph the solution
On a number line:
- Draw an
open circle at $ x = 3 $ because the inequality is
strict (no equality).
- Shade all numbers
to the left of 3, since $ x < 3 $.
This matches the number line shown in the image, where:
- The open circle is at 3.
- The shaded region extends to the left (negative direction).
---
✔ Final Answer:
$$
\boxed{x < 3}
$$
This means all real numbers less than 3 satisfy the inequality.
Parent Tip: Review the logic above to help your child master the concept of solving inequalities worksheet kuta.
